Final answer:
Upon examination of the expressions, D. x +9y² is the only expression that cannot be factored and is therefore a prime polynomial.
Step-by-step explanation:
The question asks to identify which of the given expressions is a prime polynomial. A prime polynomial is one that cannot be factored into polynomials of lower degree with integer coefficients. Let us analyze the options:
- A. 19 – 46: This is a constant expression, not a polynomial, and thus not a prime polynomial.
- B. 3m + 9n: This expression can be factored as 3(m + 3n), therefore it is not prime.
- C. 8x⁷ – 9x + 12x²: This polynomial is of higher degree and may potentially be factored further, so it needs to be examined, but it is not clearly prime without further investigation.
- D. x + 9y²: This polynomial cannot be factored into other polynomials with integer coefficients, making it a prime polynomial.
Based on the definitions and examinations, the expression D. x + 9y² is the prime polynomial.